Grafting hyperbolic metrics and Eisenstein series

Abstract

The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non holomorphic Eisenstein series $E(\zeta ;2)$ are combined to provide an explicit expansion for the hyperbolic metrics for degenerating families of Riemann surfaces. Applications include an asymptotic expansion for the Weil-Petersson metric and a local form of symplectic reduction.

Published in Mathematischen Annalen, 2008. The original publication is available at http://www.springerlink.com

References in corpus (2)

• The Weil-Petersson metric geometry
• Behavior of geodesic-length functions on Teichmueller space